Abstract
In this theoretical study, based on a nonlinear wave equation describing the interaction of fields of an X-ray laser beam with relativistic quantum plasma, modulation instability and formation of solitary waves are investigated. Analytical expressions are derived for the growth rate of modulation instability and electromagnetic envelope solitons. The frequency interval of instability and the dependence of the growth rate on some physical parameters such as the initial laser beam amplitude and frequency are considered. Additionally, the effect of the laser amplitude on the solitary waves is studied. It is shown that quantum effects lead to the reduction of nonlinearity of plasma.
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